It can stand on its own just fine. Especially considering names like Bella, Stella, Ella. I"m not very fond of the name though. It feels a bit flimsy to me, which is probably due to the Italian "della" meaning "of" / "of the".
I'm looking at Della as being based on Adela, so it can mean "noble". That way it's not as flimsy. I don't like Adela, but if you look at Della as a variant, sort of how Lucy is a variant of Lucia, then you can see more in it. What do you think?